Multiplication and factorization A 2-B 2 = (A+B) (A-B) A 3+B 3 = (A+B) (A 2-AB+B 2) A 3-B 3 = (A 2+AB+) => -b ≤ a ≤ b | a-b |≥| a |-b |-a |≤ a ≤| the solution of a quadratic equation -b+√(B2-4ac)/2a-b-√(B2-4ac)/2a root and coefficient x6544. 0 Note: The equation has two unequal real roots? b^2-4ac<； 0 Note: The equation has no real root, but a * * yoke, formulas with multiple trigonometric function angles and formulas SIN (a+b) = SINA COSB+COSA SINB SIN (a-b) = SINA COSB-SINB COSA? cos(A+B)= cosa cosb-Sina sinb cos(A-B)= cosa cosb+Sina sinb tan(A+B)=(tanA+tanB)/( 1-tanA tanB)tan(A-B)=(tanA-tanB)/( 1+tanA tanB)cot(A+B)=(cotA cotB- 1)/(cotA)？ Cot (a-b) = (cota cotb+1)/(cotb-cota) multiple angle formula tan2a = 2tana/[1-(tana) 2] cos2a = (COSA) 2-(sin (a/) 2 = 2 (. 2)=√(( 1-cosA)/2)sin(A/2)=-√(( 1-cosA)/2)cos(A/2)=√(( 1+cosA)/2)cos(A)=-√(( 1+cosA)/2)=√(( 1-cosA)/(( 1 +cosA))tan(A sum difference product 2Sina COSB = SIN (A+B)+SIN (A-B) 2Sa SINB = SIN (A+B)-SIN (A-B)) 2Sa COSB = COS (A+B)-2Sina. Cos ((a-b)/2 COSA+COSB = 2 COS ((a+b)/2) SIN ((a-b)/2) Tana +TANB = SIN (a+b)/COSA COSB and the first n terms 1+2+3+4+. 2 1+3+5+7+9+ 1 1+ 13+ 15+……+(2n- 1)= N2 2+4+6+8+ 10+ 12+ 14+……+(2n)= n(n+ 1) 5 1^2+2^2+3^2+4^2+5^2+6^2+7^2+8^2+…+n^2=n(n+ 1)(2n+ 1)/6 1^3+2^3+3^3+4^3+5^3+6^3+…n^3=n2(n+ 1)2/ 4 65438+ is the general equation X 2+Y 2+DX+EY+F = 0 Note: D 2+E 2-4f > 0 Parabolic standard equation Y 2 = 2px y 2 =-2px x 2 =-2py Right prism side area S=c*h Oblique prism side area S=c'*h Right pyramid side area S =/kloc. H' side area of regular prism S = 1/2 (c L=pi(R+r)l surface area of sphere S = 4pi number of central angles r > 0° sector area formula s= 1/2*l*r cone volume formula v =1/3 * s *. Oblique prism volume V=S'L Note: where s' is the straight cross-sectional area, and l is the volume formula of a long cylinder with side V=s*h cylinder V=pi*r2h series Basic formula: 9. The relationship between the general term an and the first n terms of general series and Sn: an= 10, and the general term formula of arithmetic progression: an = a 1. When d=0, an is constant. 1 1, the first n term of arithmetic progression and its formula: Sn = Sn = when d≠0, sn is a quadratic form about n, and the constant term is 0; When d=0 (a 1≠0), Sn=na 1 is the direct proportion formula of n 12 and the general formula of geometric series: an = a 1 qn-/an = akqn-k. Sequences Sm, S2m-Sm, S3m-S2m, S4m-S3m, ... are composed of arithmetic, and the sum {an} of the conclusion of geometric series 14 and any continuous m terms of arithmetic series is still an arithmetic series. In 15 and arithmetic progression {an}, if m+n=p+q, then in 16 and geometric progression {an}, if m+n=p+q, then the series Sm and S2formed by the sum of any continuous m terms of 17 and geometric progression {an}. 18, the sum and difference of two arithmetic progression {an} and {bn} series {an+bn} is still arithmetic progression. 19, the sequence {an bn} consisting of the product, quotient and reciprocal of two geometric series {an} and {bn} is still a geometric series. 20. arithmetic progression {an} Any equidistant series is still arithmetic progression. 2 1, the series of any equidistant term of geometric progression {an} is still geometric progression. 22. How to make three numbers equal: A-D, A, A+D; How to make four numbers equal: A-3D, A-D, A+D, A+3D23, and how to make three numbers equal: A/Q, A, AQ; Wrong method of four numbers being equal: a/q3, a/q, aq, aq3 (Why? 24. If {an} is arithmetic progression, then (c >；; 0) is a geometric series. 25 、{ bn }(bn & gt； 0) is a geometric series, then {logcbn} (c >; 0 and c 1) are arithmetic progression. 26. In arithmetic progression: (1) If the number of items is 0, then (2) If the number of items is 0, then, 27. In geometric series: (1) If the number is 0, then (2) If the number is 0, then, 4. The common methods of sequence summation: formula method, split item elimination method, dislocation subtraction method. The key is to find the general item structure of the sequence. 28. Sum the sequence by grouping: for example, an=2n+3n 29, sum by dislocation subtraction: for example, an=(2n- 1)2n 30, sum by split terms: for example, an =1/n (n+1) 31,and reverse phase. 0) For example, an= ③ an=f(n) Study the increase and decrease of function f(n) for example, an= 33. In arithmetic progression, the problem about the maximum value of Sn is usually solved by the adjacent term sign change method: (1) When >: 0, d<0, and the number of terms m satisfies the maximum value. (2) When